Free vibrations and parametric instability of a laterally loaded cable

In this paper a linear analysis is presented for the coupled vertical, longitudinal and lateral oscillations of a cable with a small sag-to-span ratio. Generally, the lateral oscillations are treated as uncoupled from the motion in the other directions. In the present study it is shown that existence of initial lateral displacement can induce coupling of all the oscillations in the three directions. The effect of a periodic component in the lateral load on the dynamic stability of the cable is also investigated